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sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([24, -1, 1]))
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pari:K = nfinit(Polrev(%s));
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magma:R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R!%s);
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oscar:Qx, x = polynomial_ring(QQ); K, a = number_field(Qx(%s))
Generator \(a\), with minimal polynomial
\( x^{2} - x + 24 \); class number \(8\).
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sage:E = EllipticCurve([K([0,0]),K([1,0]),K([0,0]),K([392,0]),K([-21712,0])])
E.isogeny_class()
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sage:E.rank()
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magma:Rank(E);
The elliptic curves in class 576.11-d have
rank \( 1 \).
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sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 2 & 8 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
2 & 4 & 2 & 1 & 4 & 2 \\
8 & 4 & 2 & 4 & 1 & 8 \\
4 & 8 & 4 & 2 & 8 & 1
\end{array}\right)\)
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sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 576.11-d over \(\Q(\sqrt{-95}) \)
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sage:E.isogeny_class().curves
Isogeny class 576.11-d contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 576.11-d1
| \( \bigl[0\) , \( 1\) , \( 0\) , \( 392\) , \( -21712\bigr] \)
|
| 576.11-d2
| \( \bigl[0\) , \( 1\) , \( 0\) , \( 17\) , \( 38\bigr] \)
|
| 576.11-d3
| \( \bigl[0\) , \( 1\) , \( 0\) , \( -108\) , \( 288\bigr] \)
|
| 576.11-d4
| \( \bigl[0\) , \( 1\) , \( 0\) , \( -608\) , \( -5712\bigr] \)
|
| 576.11-d5
| \( \bigl[0\) , \( 1\) , \( 0\) , \( -1608\) , \( 24288\bigr] \)
|
| 576.11-d6
| \( \bigl[0\) , \( 1\) , \( 0\) , \( -9608\) , \( -365712\bigr] \)
|
